CHICAGO — Pope Francis will face the daunting task of helping unite a U.S. church caught in a tug of war between traditionalists and progressives on issues such as contraception, same-sex marriage and married priests.

U.S. Catholics seemed largely optimistic about the new pope, but some are taking a “wait and see” approach to a leader known to be a strict traditionalist.

In the United States, the results of November’s presidential election highlighted the divide between Catholics who want the church to modernize and those who favor its traditional ways. U.S. Catholic bishops pushed hard against policies favoring gay marriage and contraception, warning of the “intrinsic evils” of the Democratic platform. But postelection polling showed that most Catholics favored President Barack Obama.

Maureen Ferguson, senior policy adviser for the Catholic Association, a lay group that advocates conservative social policies, said she does not think the new pope belongs in a “box” labeled traditional or progressive.

“He has this personal simplicity, yet he holds this high office in the church,” said Ferguson. “He spoke out in Argentina against allowing same-sex couples to adopt, yet he goes to the hospice and washes the feet of AIDS patients, which embodies the teaching that every person has a home in the church.”

Nicholas Cafardi, dean emeritus at Duquesne University Law School in Pittsburgh and a civil and canon lawyer, agrees that Francis is tough to classify.

“He’s a Jesuit — Jesuits are known as men of education, men of ideas, men who aren’t afraid to confront opposing ideas, and at the same time, he’s certainly been very orthodox himself in his teachings,” Cafardi said.

About 25 percent of U.S. residents are Roman Catholic, but that number has been buoyed by a continuing influx of Hispanic immigrants. Lapsed Catholics have become the nation’s second-largest religious classification, after Catholics, representing 10 percent of U.S. residents, according to the Pew Forum on Religion & Public Life.

A 2012 Gallup poll found that 82 percent of U.S. Catholics found birth control morally acceptable, even though it is prohibited by the church.

Most Catholics surveyed, 54 percent, also support gay marriage, compared with 47 percent of all Americans, according to a Quinnipiac University poll released this month.